Fineness Modulus Calculator
Fineness modulus per NBR NM 248 with NBR 7211 grading zones for fine aggregate.
Calculator
Normal series — retained masses
Theory & method
The fineness modulus (FM) is a single-number index of the coarseness of an aggregate, defined in NBR NM 248 (and analogously in ASTM C136/C125) as the sum of the cumulative retained percentages on the sieves of the normal series, divided by 100. For fine aggregate the normal series is 4.75 mm, 2.36 mm, 1.18 mm, 0.60 mm, 0.30 mm and 0.15 mm.
Intermediate sieves (such as 6.3 mm) may be used in the test and appear on the grading curve, but they are never included in the FM sum — a common source of calculation errors. Likewise, a sieve on which no material is retained still counts in the series with 0% retained; omitting it changes nothing in the sum but omitting a sieve that does retain mass invalidates the result.
A higher FM means a coarser sand. NBR 7211 uses the FM together with per-sieve grading limits to frame fine aggregate for concrete: the optimal zone corresponds to FM between 2.20 and 2.90, and the usable zone extends from 1.55 to 3.35. Sands outside these bounds may still be used, but require mix-design justification.
The test itself follows NBR NM 248: a dried sample is sieved, the retained mass on each sieve is weighed, and the difference between the initial mass and the sum after sieving must not exceed 0.3% — otherwise the test is invalid. This calculator applies that mass-loss check automatically when you provide the initial sample mass.
How to use
- 01Enter the dry retained mass (in grams) on each sieve of the normal series: 4.75, 2.36, 1.18, 0.60, 0.30 and 0.15 mm. Use 0 for sieves that retained no material — do not leave real retentions out.
- 02Enter the mass collected in the pan (bottom receiver).
- 03Optionally enter the initial dry sample mass to validate the 0.3% mass-loss criterion of NBR NM 248.
- 04Read the fineness modulus and the NBR 7211 zone classification (optimal, usable, or outside the zones), together with the cumulative retained percentages used in the sum.
Frequently asked questions
Which sieves enter the fineness modulus sum?
Only the normal-series sieves: 4.75, 2.36, 1.18, 0.60, 0.30 and 0.15 mm for fine aggregate. Intermediate sieves (e.g. 6.3 mm) belong to the test and the grading curve, but are excluded from the FM sum by definition (NBR NM 248 §3.2).
What is a good fineness modulus for concrete sand?
NBR 7211 places the optimal zone at FM 2.20–2.90 and the usable zone at 1.55–3.35. Within the optimal zone the sand grading is considered well suited for conventional concrete; in the usable zone it remains acceptable with mix adjustments.
Why does the calculator reject my input when a sieve is missing?
Assuming zero retention on a sieve that was simply not reported would silently distort the cumulative percentages and the FM. Following the fail-fast policy of this site's calculation engine, every normal-series sieve must be reported explicitly — 0 g is a valid entry.
How is the 0.3% mass-loss criterion applied?
NBR NM 248 (like ASTM C136 §9.2) invalidates the test when the difference between the initial dry mass and the sum of retained masses plus pan exceeds 0.3%. If you provide the initial mass, the calculator flags the result as acceptable or not.
Normative references
- ABNT NBR NM 248:2003 — Agregados — Determinação da composição granulométrica.
- ABNT NBR 7211:2022 — Agregados para concreto — Requisitos (zonas ótima e utilizável do agregado miúdo).
- ASTM C136/C136M-19 — Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates.
- ASTM C125 — Standard Terminology Relating to Concrete and Concrete Aggregates (fineness modulus).